Ferromagnetism in correlated electron systems: Generalization of Nagaoka's theorem.

Nagaoka’s theorem on ferromagnetism in the Hubbard model with one electron fewer than half filling is generalized to the case where all possible nearest-neighbor Coulomb interactions ~the density-density interaction V , bond-charge interaction X , exchange interaction F , and hopping of double occupancies F8) are included. It is shown that for ferromagnetic exchange coupling (F.0) ground states with maximum spin are stable already at finite Hubbard interaction U.Uc . For nonbipartite lattices this requires a hopping amplitude t<0. For vanishing F one obtains Uc→` as in Nagaoka’s theorem. This shows that the exchange interaction F is important for stabilizing ferromagnetism at finite U . Only in the special case X5t is the ferromagnetic state stable even for F50, provided the lattice allows the hole to move around loops.